Mortgage, Credit and the Price You Pay: A Mortgage Simulation

• Use the concept of an interest rate to identify a percent change in an exponential function.
• Use the exponential function of a mortgage payment formula to model a monthly mortgage payment and the amount of money paid over time.

And in the realm of personal finance:

• Identify the financial impacts of taking out a longer loan or having fair or poor credit.

Exponential functions are one of the function families heavily emphasized in an Algebra 2 curriculum. The purpose of this lesson is to get students to interact with a real life exponential function while also learning about the personal financial decisions of maintaining credit and taking out a mortgage.

Students will be assessed according to the rubric for the project. Some of the milestones that are included in the rubric are: 

• Expresses interest rate as a percentage in decimal form (and computation of the monthly interest rate).
• Chooses the appropriate formula to compute the monthly payment vs. the total amount paid over time.
• Utilizes appropriate values to substitute in for each variable.

• Mortgage Simulation Introduction – A bellwork that gets students thinking about the mortgage project without using much math and more common sense. Be sure to make your own copy of this form so you have access to your students’ responses.
• Credit “Cards” – To make this a simulation, I made “credit cards” for each student to choose at random. By randomness, students will choose the level of credit that they will be assigned for their project.
• Mortgage Project Packet – This is the packet in which students will submit their dream home, the computations of their monthly payments, and mortgage payments.

Bellwork (10 minutes)

Students will be presented with the introduction to the Mortgage Simulation by actually going through a real life mortgage scenario. They will have to choose 2 options (a 15 year vs. a 30 year mortgage) without thinking in detail about the mathematics. I explicitly tell students that I am not looking for a right/wrong answer. The barrier to entry for this bellwork is purposefully low as many students will enter the grownup world thinking about interest rates.

Bellwork Discussion (10 minutes)

Peer to Peer: If you want some inter-peer collaboration, you can do a turn and talk after students have submitted their Google Form. If you are to do a turn and talk, you can ask a question like: “tell your peer whether you chose option 1 or 2 and why?”

Whole Class: I utilize Google Forms purposefully as I like to have the data coming in from students. This can motivate a whole class discussion about interest rates. I would read sample responses and rationales. I also would strategically call on students who chose option 1 and option 2 to present both viewpoints for why students would choose either option.

Project Work Time (40 minutes)

Part 1: Choosing a Dream Home and Credit Score Assignment (10-15 minutes)

My suggestion would be to have multiple checkpoints for students to hold them accountable for working at a reasonable pace. Students might be tempted to spend large amounts of time surfing the web on houses. This is a double edged sword as it is fun for the students to choose their dream home, but is a time waster if this is abused.

Students should copy the price of the home and put in a picture of the listing of their home. Upon the students choosing their home, you can have students choose their “credit card” out of a hat. This “credit card” will give the students their credit score.

Part 2: Computing the interest rate (5-10 minutes)

Once students get their credit score, they will need to compute their interest rate based on their credit score and also compute the monthly interest on an excellent credit score interest rate.

On-grade-level students and above generally connect the interest rate percentage with the decimal form without much help. You will need to spend some time coaching your below grade students in figuring out the percentages (oftentimes, struggling students have trouble converting 4 percent to 0.04 in a formula). However, most of these students can rise to this task with some help. Additionally, this could be done if a teacher pairs a higher level student with a lower level student.

Part 3: Computations (15-20 minutes)

Using the given formula and a calculator, students will compute what their monthly payment for their dream home is as well as the total amount paid over time. You will want to make sure that students know what the variables stand for in the formula (i.e. r is an interest rate that is written in decimal form, and t is the number of months).

If you have a class with a high number of resource students, ENL students, and/or below grade level students, you might want to show students a sample calculation based on a sample dream home. Often, I have found that lower level students are better able to access non-linear functions (i.e. exponentials, logarithmic, square root functions) when they are able to see patterns in the form of the equation.

Part 4: Reflection (15 minutes)

When students show you that they are done with the computation, have the students show you their computation to check their work. If all looks good, then tell them to write at least one paragraph about lessons learned from their exercise.

Extensions (to enrich the use of technology or the scope of discussion)

• When I did this project a few years ago in a summer school-type class setting, I took my students to downtown Indianapolis where students went into various banks (i.e. Huntington and Chase) to ask what the going interest rates were on a mortgage.
• This lesson could have cross curricular features with an extension to housing discrimination throughout US History. In going this route, you might want to: 
  • Start with a video like Housing Discrimination Causes Generational Wealth Gap Between Black and White Americans
  • Modify the Introductory Bellwork to include discussion questions surrounding the above video like: “do you think credit score is the only factor that goes into what interest rate someone gets?”. This modification could also be made in the reflection section as well. Deciding to include such an extension in the bellwork or reflection piece would increase the amount of time you would need to spend on those items.
  • I recommend consulting your local social studies teacher, instructional coach, or administrator to brainstorm ideas as to how to best lead the discussion. 
• Use a tool like FlipGrid or the RECORD feature on Zoom for students to create YouTube-style videos.
  • If you are teaching a class with mathematically mature students, having students create videos on how to compute their monthly payment and total paid overtime can really help develop and hone in on mathematical communication skills. 
  • If you want a FlipGrid/video making to be less mathematically elaborate and more reflective, you could make a FlipGrid option for the Written Reflection piece where students summarize lessons learned from the project on FlipGrid.

From Indiana’s Algebra 2 Standards

AII.EL.3 Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

AII.EL.4 Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.